If the distance between the foci


If the distance between the foci of a hyperbola is 16 and its eccentricity is √2, then obtain the equation of the hyperbola.


We know that equation of Hyperbola


Also we have foci $=(\pm a e, 0)$

Given distance between foci is $2 \mathrm{ae}=16$


$2 \times a \times \sqrt{2}=16$

$a=\frac{16}{2 \times \sqrt{2}}=\frac{8}{\sqrt{2}}=4 \sqrt{2}$

$\because b^{2}=a^{2}\left(e^{2}-1\right)$

$\mathrm{b}^{2}=(4 \sqrt{2})^{2}\left((\sqrt{2})^{2}-1\right)$


$\therefore$ Equation is $\frac{x^{2}}{32}-\frac{y^{2}}{32}=1$

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